Power, Levy, Exponential and Gaussian Regimes in Autocatalytic Financial Systems
AbstractWe study by theoretical analysis and by direct numerical simulation the dynamics of a wide class of asynchronous stochastic systems composed of many autocatalytic degrees of freedom. We describe the generic emergence of truncated power laws in the size distribution of their individual elements. The exponents $\alpha$ of these power laws are time independent and depend only on the way the elements with very small values are treated. These truncated power laws determine the collective time evolution of the system. In particular the global stochastic fluctuations of the system differ from the normal Gaussian noise according to the time and size scales at which these fluctuations are considered. We describe the ranges in which these fluctuations are parameterized respectively by: the Levy regime $\alpha 2$), and the exponential decay. Finally we relate these results to the large exponent power laws found in the actual behavior of the stock markets and to the exponential cut-off detected in certain recent measurement.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by arXiv.org in its series Papers with number cond-mat/0008026.
Date of creation: Aug 2000
Date of revision:
Publication status: Published in Eur. Phys. J. B 20 (2001) 601-607
Contact details of provider:
Web page: http://arxiv.org/
Other versions of this item:
- Zhi-Feng Huang, Sorin Solomon*, 2001. "Power, Levy, Exponential and Gaussian Regimes in Autocatalytic Financial Systems," Computing in Economics and Finance 2001 12, Society for Computational Economics.
You can help add them by filling out this form.
CitEc Project, subscribe to its RSS feed for this item.
- Marco Raberto & Silvano Cincotti & Sergio Focardi & Michele Marchesi, 2003.
"Traders' Long-Run Wealth in an Artificial Financial Market,"
Society for Computational Economics, vol. 22(2), pages 255-272, October.
- Marco Raberto & Silvano Cincott & Sergio M. Focardi & Michele Marchesi, 2002. "Traders’ long-run wealth in an artificial financial market," Computing in Economics and Finance 2002 301, Society for Computational Economics.
- Masanao Aoki & Hiroshi Yoshikawa, 2006. "Stock Prices and the Real Economy: Power Law versus Exponential Distributions," Journal of Economic Interaction and Coordination, Springer, vol. 1(1), pages 45-73, May.
- Masanao Aoki, 2006. "Thermodynamic Limits of Macroeconomic or Financial Models: One-and Two-Parameter Poisson-Dirichlet Models (Forthcoming in "Journal of Economic Dynamics and Control", 2007. )," CARF F-Series CARF-F-083, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators).
If references are entirely missing, you can add them using this form.